Daily and Intradaily Stochastic Covariance:
Value at Risk Estimates for the Foreign Exchange Market
George Komas
The importance of time varying voIatility in securities prices (e.g. GARCH) has
by now been arnply established in the literature, both in terrns of the magnitude
and pervasiveness of the phenomenon, and in terms of its significance for risk
management in institutional portfolios. Less attention has been devoted to
multivariate conditional heteroskedasticity, in spite of the fact that secwities are
typically held in portfolios rather than in isolation. Recently, Kroner and Ng
(1995) have introduced a method for nesting the four most commonly used
multivariate GARCH models, allowing for comparative tests of the performance
of the models. We propose to apply the Kroner and Ng technique to both daily
and intradaily returns on foreign exchange rates, to obtain performance
estimates. These conditional covariances will then be used to calculate value at
risk (VaR) forecasts for foreign currency portfolios. Daily and intradaily VaR
forecasts will be evaluated and compared.